Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion

Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped Cd-111(+) ion, and show that phase coherence of the resulting entangled states of spin and motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.